Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y= 8/sqareroot of 2x+4
f(x) = 8, g(x) = square root of quantity two x plus four.
f(x) = square root of quantity two x plus four., g(x) = 8
f(x) = eight divided by x., g(x) = 2x + 4
f(x) = eight divided by square root of x., g(x) = 2x + 4

Answer:

The acceleration of the object is 4 [tex]m/s^2[/tex]

Step-by-step explanation:

Given:

The mass of the object is = 2 kg

To Find:

Acceleration of the object = ?

Solution:

From the diagram below we know that

The resultant force is 8N along the east Direction

we know the acceleration is the"Rate of change of Velocity"

And Expressed as

F = ma

Where

F is the Force

m is the mass

Now substituting the known values we get

[tex]8 = 2 \times a[/tex]

[tex]a =\frac{8}{2}[/tex]

a=4 [tex]m/s^2[/tex]

Answer:

b the object is 4 m/s

Step-by-step explanation:

Two buckets of seawater contain [tex]13\frac{28}{40}[/tex] kg of salt.

Step-by-step explanation:

Amount of salt in 1 kg water = [tex]\frac{1}{40}\ kg[/tex]

It is given that;

1 liter = [tex]1\frac{12}{125} = \frac{137}{125}\ kg[/tex]

500 liters = [tex]500*\frac{137}{125} = \frac{68500}{125}[/tex]

500 liters = 548 kilogram

As,

1 kg of seawater = [tex]\frac{1}{40}\ kg[/tex] of salt

548 kilograms = [tex]\frac{1}{40}*548[/tex]

548 kilograms = [tex]13\frac{28}{40}[/tex] kilograms of salt

Two buckets of seawater contain [tex]13\frac{28}{40}[/tex] kg of salt.

Keywords: unit rate, multiplication

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Answer:

$768

Step-by-step explanation:

Let x bet the cost of 124 training session.

Given:

Maria finds a local gym that advertises 101 training sessions for $626.

Find the cost of 124 training sessions.

Solution:

cost for each training sessions [tex]=\frac{626}{101}[/tex]

cost for each training session = $6.19

So, we get cost of 124 training sessions by multiplication of cost of each training sessions and number of training sessions.

[tex]x=cost\ of\ each\ training\ session\times number\ of\ training\ session[/tex]

[tex]x=6.19\times 124[/tex]

[tex]x=767.56[/tex]

round 767.56≅768

[tex]x=768[/tex]

Therefore, the cost of 124 training sessions is $768

Answer:

Y(n) = 7n + 23

Step-by-step explanation:

Given:

f(0) = 30

f(n+1) = f(n) + 7

For n=0 : f(1) = f(0) + 7

For n=1 :  f(2) = f(1) + 7

For n=2 : f(3) = f(2) + 7 and so on.

Hence the sequence is an arithmetic progression with common difference 7 and first term 30.

We have to find a general equation representing the terms of the sequence.

General term of an arithmetic progression is:

T(n) = a + (n-1)d

Here a = 30 and d = 7

Y(n) = 30 + 7(n-1) = 7n + 23

Answer:

(i) [tex]k\in (-\infty,-16)\cup (0,\infty)[/tex]

(ii) [tex]p\in (9,\infty)[/tex]

Step-by-step explanation:

(i) Given equation

[tex]2x^2+4x+2=k(x+3)[/tex]

Rewrite this equation as quadratic equation in the standard form:

[tex]2x^2+4x+2=kx+3k\\ \\2x^2+4x+2-kx-3k=0\\ \\2x^2+(4-k)x+(2-3k)=0[/tex]

If the equation has two distinct real roots, then its discriminant is greater than 0. Find the discriminant:

[tex]D=(4-k)^2-4\cdot 2\cdot (2-3k)=16-8k+k^2-16+24k=k^2+16k[/tex]

Solve the inequality [tex]D>0:[/tex]

[tex]k^2+16k>0\\ \\k(k+16)>0\Rightarrow k\in (-\infty,-16)\cup (0,\infty)[/tex]

(ii) The quadratic expression is always greater than 0 when:

[tex]p>0\\ \\D<0[/tex]

Find the discriminant:

[tex]D=6^2-4\cdot p\cdot 1=36-4p[/tex]

Solve the inequality [tex]D<0:[/tex]

[tex]36-4p<0\\ \\-4p<-36\\ \\4p>36\\ \\p>9[/tex]

Assuming that [tex]p>0[/tex] and [tex]p>9,[/tex] you get

[tex]p>9\Rightarrow p\in (9,\infty)[/tex]

I think you mean [tex]\sqrt{68}[/tex] so I will just simplify that.

[tex]\sqrt{68}=\sqrt{4}*\sqrt{17}=2\sqrt{17}[/tex]

answer: [tex]2\sqrt{17}[/tex]

the answer is 2√17

hope this helps :)))

Answer:

[tex]f(5)=f(1)+12[/tex]

Step-by-step explanation:

If [tex]f(5) = f(4) + 3,[/tex] then

[tex]f(n)=f(n-1)+3[/tex]

So,

[tex]f(2)=f(2-1)+3=f(1)+3\\ \\f(3)=f(3-1)+3=f(2)+3=f(1)+3+3=f(1)+6\\ \\f(4)=f(4-1)+3=f(3)+3=f(1)+6+3=f(1)+9\\ \\f(5)=f(5-1)+3=f(4)+3=f(1)+9+3=f(1)+12[/tex]

Answer:f(5) = f(1) + 12

Step-by-step explanation:

Final answer:

The resulting solid will have four edges.

Explanation:

To find the number of edges in the resulting solid, let's first determine the dimensions of the solid after the wedges are cut off.

The original wooden block measures 2 inches by 2 inches by 3 inches. After cutting off the wedges, each side will be reduced by 2 inches (1 inch from each corner), resulting in a solid with dimensions of 2 - 2(1) = 0 inches by 2 - 2(1) = 0 inches by 3 - 2(1) = 1 inch.

A solid with dimensions of 0 inches by 0 inches by 1 inch is essentially a rectangular prism with one dimension equal to zero. Such a solid has six faces, eight vertices, and four edges.

Therefore, the resulting solid will have four edges.

Answer:

The equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.

Step-by-step explanation:

As the sentence statement is

"Two more than 1/3 of number is eight".

Lets decode this sentence and write the corresponding mathematical expression.

Hence, the equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.

Keywords: equation, algebraic expression

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Answer:

19.6 gallons.

Step-by-step explanation:

She drives 225/ 10 = 22.5 miles per gallon of gas.

So driving 441 miles she will use 441/22.5

= 19.6 gallons.

Answer:

∠3 = 135°

Step-by-step explanation:

∠3 = ∠1 = 135° ( corresponding angles are congruent )

The best use of a sign chart when graphing rational functions involves identifying critical points, determining function values within each interval, and using this information to sketch the graph. The sign chart is a valuable tool for analyzing the behavior of a rational function on the x-axis.

The sign chart is a useful tool when graphing rational functions because it helps identify the intervals where the function is positive, negative, or undefined. This information is crucial for accurately sketching the graph of a rational function. Here is how to use a sign chart:

Identify the critical points of the function by setting the numerator and denominator equal to zero and solving for the variables.

Choose a value from each interval determined by the critical points and evaluate whether the function is positive or negative at that value.

Record the signs in a table or chart to visualize the pattern.

Use the sign chart to determine the intervals on the x-axis where the function is positive, negative, or undefined.

Plot any vertical asymptotes, holes, and x-intercepts on the graph.

Sketch the graph by using the information from the sign chart and locating the appropriate points.

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Answer:

[tex]\frac{1}{20}[/tex]

Step-by-step explanation:

First, we need to look at the # of chips. There are a total of 25, 6 of which are blue.

This means that the chance of getting the first blue chip would be [tex]\frac{6}{25}[/tex]

As there is no replacement, the total number of chips is 24 and there are only 5 blue left. This gives us the chance of [tex]\frac{5}{24}[/tex]

Now all we need to do is mulitply these two and then simplify

[tex]\frac{6}{25} *\frac{5}{24} =\frac{30}{600} =\frac{1}{20}[/tex]

Answer:

1/20

Step-by-step explanatio

pick without replacement must mean pick it two times without put back the first chip

6/25 x 5/24 = 1/20

Answer: 105.26

Step-by-step explanation: 9263/88=105.26

Do you have or own a calculator?

s>7

So, all values greater than 7 are included in the number line.

Step-by-step explanation:

We need to use number line to show numbers in the solution set of the inequality 2s+ 36 greater than 50

Solving and finding value of s:

2s+36>50

Adding -36 on both sides

2s+36-36>50-36

2s>14

Divide both sides by 2

s>7

So, all values greater than 7 are included in the number line.

The number line is shown in figure attached below

Keywords: Solving inequalities

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Answer:

A

Step-by-step explanation:

Took the test in edge

Answer:

Second table

Step-by-step explanation:

Proportional relationships between x and y satisfied the following equation y = k*x, where k is some constant. Rearranging we get: k = y/x. So, if we take every pair y-x and divided them, we have to find the same k.

- Division y/x for the first table:

2/1 = 2

5/3

8/4 = 2

14/7 = 2       It is not a proportional relationship

- Division y/x for the second table:

1/7

2/14 = 1/7

4/28 = 1/7

5/35 = 1/7       It is a proportional relationship

- Division y/x for the third table:

4/1 = 4

10/2 = 5

12/3 = 4

16/4 = 4        It is not a proportional relationship

- Division y/x for the fourth table:

5/2.5 = 2

6/3 = 2

10/5 = 2

15/6 = 5/2        It is not a proportional relationship

Answer:

x = 11, y = 3

Step-by-step explanation:

9x + 25 and 13x - 19 are corresponding angles and congruent, thus

13x - 19 = 9x + 25 ( subtract 9x from both sides )

4x - 19 = 25 ( add 19 to both sides )

4x = 44 ( divide both sides by 4 )

x = 11

Thus

13x - 19 = (13 × 11) - 19 = 143 - 19 = 124°

13x- 19 and 17y + 5 form a straight angle and are supplementary, thus

13x - 19 + 17y + 5 = 180, that is

124 + 17y + 5 = 180

129 + 17y = 180 ( subtract 129 from both sides )

17y = 51 ( divide both sides by 17 )

y = 3

Answer:

The next 3 steps are

Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]

Step 5: [tex]x=-2\pm \sqrt{10}[/tex]

Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]

Step-by-step explanation:

Given:

Quadratic Equation is

x² + 4x - 6 = 0

To Find:

x = ?

Solution:

Step 1: x2 + 4x = 6

Step 2: x2 + 4x + 4 = 6 + 4

Step 3: (x + 2)2 = 10

Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]

Step 5: [tex]x=-2\pm \sqrt{10}[/tex]

Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]

Please the attachment for question.

Answer:

Measurement of JL=8

Step-by-step explanation:

Given:-

[tex]\triangle JKL\ is\ right\ angle\ triangle[/tex]

[tex]m\angle J=62\ degree[/tex]

JK=17

[tex]sin\ 62\ degree= 0.88[/tex]

[tex]cos\ 62\ degree= 0.47[/tex]

[tex]tan\ 62\ degree= 1.88[/tex]

To find measurement of JL=?

Now,

[tex]cos\theta=\frac{adjacent\ side}{hypotenuse}[/tex]

[tex]cos\ 62\ degree=\frac{JL}{17}[/tex]

[tex]0.47=\frac{JL}{17}[/tex]

[tex]JL=0.47\times 17[/tex]

[tex]JL=7.99[/tex]

[tex]JL=8[/tex]

Therefore measurement of JL=8

Answer:

White.

Step-by-step explanation:

Theoretical probabilities are:

Red: 5 / ( 5 + 6 + 5) = 5/16

White: 6/16 = 3/8.

Blue:  5/16.

The answer is white because it is drawn 12 times which equals its  theoretical probability: 12/32 = 3/8.

The probability of drawing the color the same as the theoretical probability is 3/8.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A bag contains 5 red, 6 white, and 5 blue marbles.

Theoretical probabilities for the colors are:

Red:

= 5 / ( 5 + 6 + 5)

= 5/16

White:

= 6/16

= 3/8.

Blue:  5/16.

So, the probability of drawing the color the same as the theoretical probability  is white because the theoretical probability is 3/8.

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The question is missing the graph. So, it is attached below.

Answer:

(D) 3.2

Step-by-step explanation:

Given:

A graph of height versus width.

The equation given is:

Height = constant × Width

Rewriting in terms of 'constant'. This gives,

[tex]\textrm{Constant}=\frac{Height}{Width}[/tex]------------- (1)  

The width is plotted on the X-axis and the corresponding height is plotted on the Y-axis.

The four points plotted on the line are:

[tex](x, y) = (0.5, 1.6), (1, 3.2), (2, 6.4)\ and\ (3, 9.6)[/tex].

Now, any point will satisfy equation (1).

Consider the point (0.5, 1.6). So, height = 1.6 and width = 0.5. Therefore,

[tex]\textrm{Constant}=\frac{Height}{Width}\\\\\textrm{Constant}=\frac{1.6}{0.5}=3.2[/tex]

Also, we observe that for all the remaining points,

[tex]\dfrac{3.2}{1}=\dfrac{6.4}{2}=\dfrac{9.6}{3}=3.2[/tex].

Hence, the value of the constant is 3.2.

Option (D) is correct.

Answer:

B or D ( answer = 5 => Two options is one! One of the options should be 5)

Note: The width of a rectangle will never be negative.

Answer:

its d. 5

Step-by-step explanation:

Answer:

The length of A'B' is 15 units

Step-by-step explanation:

As line segment AB has end points

The distance formula to calculate the distance between two points is given by:

[tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}[/tex]

[tex]{\displaystyle d={\sqrt {(20-4)^{2}+(4-16)^{2}}}}[/tex]

[tex]d=\sqrt{16^2+(-12)^2}[/tex]

[tex]d=\sqrt{256+144}[/tex]

[tex]d=\sqrt{400}[/tex]

[tex]d=20[/tex]

[tex]d=20[/tex] is also the length of the line segment AB.

As segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'.

So,

The length of A'B' can be obtained by multiplying the length of AB by 3/4

Therefore,

The length of A'B' = 3/4 × 20 = 15

So, the length of A'B' is 15 units.

Keywords: dilation, distance formula, length, line segment

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Answer:

[tex]x=-\frac{261}{46}[/tex]

Step-by-step explanation:

we have the expression

[tex]\frac{3x+2y-5z}{y-4z}=\frac{x}{3y}[/tex]

we have

[tex]y=6,z=-\frac{1}{2}[/tex]

To find the value of x, substitute the given values of y and z in the expression

[tex]\frac{3x+2(6)-5(-\frac{1}{2})}{6-4(-\frac{1}{2})}=\frac{x}{3(6)}[/tex]

solve for x

[tex]\frac{3x+12+\frac{5}{2}}{6+2}=\frac{x}{18}[/tex]

[tex]\frac{3x+12+\frac{5}{2}}{8}=\frac{x}{18}[/tex]

Multiplying in cross

[tex](3x+12+\frac{5}{2})18=8x[/tex]

[tex]54x+216+45=8x[/tex]

[tex]54x-8x=-216-45[/tex]

[tex]46x=-261[/tex]

[tex]x=-\frac{261}{46}[/tex]

Answer:

Weight of each large box [tex]x=15.75kg[/tex]

Weight of each small box [tex]y=13.75kg[/tex]

Step-by-step explanation:

Given:- Two equations are given,

Equation 1 :- [tex]7x+9y=234[/tex]

Equation 2:- [tex]5x+3y=120[/tex]

let,

x=weight of large box in Kilogram.

y=weight of small box in Kilogram.

Now,

multiply Equation 1 by 2 and Equation 2 by 6,

So we get 2 new equations,

Equation 3:- [tex]14x+18y=468[/tex]

Equation 4:- [tex]30x+18y=720[/tex]

Now after subtracting Equation 3 from Equation 4 we will get a new equation,

i.e. Equation 5:- [tex]16x=252[/tex]

therefore [tex]x=15.75[/tex]

now, put the value of x in Equation 1, so we will get

[tex](7x15.75)+9y=234[/tex]

[tex]110.75+9y=234[/tex]

[tex]9y=234-110.75[/tex]

[tex]9y=123.75[/tex]

[tex]y=123.75/9[/tex]

[tex]y=13.75[/tex]

So, weight of each large box i.e. [tex]x=15.75 kilogram[/tex]

and weight of each small box i.e. [tex]y=13.75 kilogram[/tex]

Complete Question with table is attached

Answer:

Miguel will save money of $90 if he earns $120.00

Step-by-step explanation:

The figure attached clearly shows the ratio of his earnings and savings. We have to find what would be the savings amount if he earn $120.00. So, first we have to calculate the percentage of ratio of his earnings and savings. As per the data given in the figure,

If he earns $10.00, he saves $7.50, calculate %amount he saves as below,

           [tex]\frac{\$ 7.50}{\$ 10.00} \times 100=0.075 \times 100=75 \%[/tex]

Likewise, calculate for all given data. If he earns $50.00 then he saves $37.50

           [tex]\frac{\$ 37.50}{\$ 50.00} \times 100=0.75 \times 100=75 \%[/tex]

If he earns  $150.00 and save $112.50,

           [tex]\frac{\$ 112.50}{\$ 150.00} \times 100=0.75 \times 100=75 \%[/tex]

So, from all above, it clearly tells that Miguel saves 75% of amount from his earnings. Now, given earnings as $120.00. By finding 75% of $120.00, we can find his savings in that amount. So,

             [tex]\frac{75}{100} \times \$ 120=0.75 \times 120=\$ 90[/tex]

Answer:

D. $90.00

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

see photo for work

Answer:

m3=43°

Step-by-step explanation:

The total has to add up to 180° so 180-137 = 43°

Answer:

11/10

Step-by-step explanation:

4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10